$b$-度量空间中两类 $(p,\xi)$-型压缩映射的不动点定理

数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 919-928.

$b$-度量空间中两类 $(p,\xi)$-型压缩映射的不动点定理

李吉红, 左占飞^*(), 黄华平

重庆三峡科技大学数学与统计学院重庆 404100

收稿日期:2025-03-14 修回日期:2025-06-25 出版日期:2026-06-26 发布日期:2026-06-16
通讯作者: 左占飞 E-mail:zuozhanfei@139.com
基金资助:
重庆市科技局面上项目(CSTB2023NSCQ-MSX0974);重庆市科技局面上项目(CSTB2022NSCQ-MSX0290);重庆三峡学院人才引进项目(20190020);研究生科研创新项目(YJSKY25030)

Fixed Point Theorems for Two Classes of $(p,\xi)$-Type Contraction Mappings in $b$-Metric Spaces

Jihong Li, Zhanfei Zuo^*(), Huaping Huang

School of Mathematics and Statistics, Chongqing Sanxia University of Science and Technology, Chongqing 404100

Received:2025-03-14 Revised:2025-06-25 Online:2026-06-26 Published:2026-06-16
Contact: Zhanfei Zuo E-mail:zuozhanfei@139.com
Supported by:
Natural Science Foundation of Chongqing(CSTB2023NSCQ-MSX0974);Natural Science Foundation of Chongqing(CSTB2022NSCQ-MSX0290);Talent Initial Funding for Scientific Research of Chongqing Three Gorges University(20190020);Postgraduate Research Innovation Project(YJSKY25030)

摘要/Abstract

摘要：

该文在 $b$-度量空间中证明了两类 $(p,\xi)$-型压缩映射的不动点存在性定理. 通过具体实例验证了存在无法应用经典 Banach 不动点定理求解不动点的情况, 但可以利用该文结论获得其不动点的存在性. 所得结果不仅改进和推广了度量空间中已有的若干不动点定理, 也为求解不动点问题提供了新的理论工具, 拓宽了不动点研究的应用范围.

关键词: $b$-度量空间, $(p,\xi)$-型压缩映射, 弱 Picard 连续, 不动点.

Abstract:

In this paper, the existence theorems of fixed points for two classes of $(p,\xi)$-type contractive mappings are proved in $b$-metric spaces. Through some concrete examples, it is verified that there exist cases where the classical Banach fixed point theorem cannot be applied to solve fixed point problems, but the existence of fixed points can be obtained by using the conclusions of this paper. The obtained results not only improve and generalize several existing fixed point theorems in metric spaces, but also provide new theoretical tools for solving fixed point problems, thereby broadening the application scope of fixed point research.

Key words: $b$-metric space, $(p,\xi)$-type contraction mapping, weakly Picard continuous, fixed point.

中图分类号:

O177.91

李吉红, 左占飞, 黄华平. $b$-度量空间中两类 $(p,\xi)$-型压缩映射的不动点定理[J]. 数学物理学报, 2026, 46(3): 919-928.

Jihong Li, Zhanfei Zuo, Huaping Huang. Fixed Point Theorems for Two Classes of $(p,\xi)$-Type Contraction Mappings in $b$-Metric Spaces[J]. Acta mathematica scientia,Series A, 2026, 46(3): 919-928.

图/表 2

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